Are there soliton-like solutions of coupled (1 + 1)- and (2 + 1)-DIM NSE?

We consider two coupled nonlinear Schrِdinger equations, the (1 + 1) and the (2 + 1)-dimensional and concentrate basically on the question as to whether there exists a stable, self-trapped solution. The positive answer is obtained within the variational and the numerical method. Namely, it is observed that neither spreading nor catastrophic self-focusing can develop and an oscillating, self-trapped solution arises. Numerical results show, in contradiction to the variational ones, that amplitudes of those oscillations decrease with propagation distance and for sufficiently large distances they vanish to zero.